Manny owns a home with a front and back lawn. The front lawn is ⅓ the size of the back lawn. If she mows ½ of her front lawn and ⅔ of her back lawn, what fraction of her entire lawn was left unmowed?

Step-by-step explanation:

The computation of the fraction of her overall lawn remaining unmowed is shown below:

Let us assume that the back lawn be x

So the front lawn would be

So, the total lawn is  ................... (i)

The back lawn mowed is

Front lawn moved is

So, the total mowed is ....................(ii)

So, the total unmowed is

Now the fraction is

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below: